Advanced Studies in Pure Mathematics

Non-homeomorphic conjugate complex varieties

Ichiro Shimada

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Abstract

We present a method to produce examples of non-homeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 285-301

Dates
Received: 8 January 2008
Revised: 8 July 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448022

Digital Object Identifier
doi:10.2969/aspm/05610285

Mathematical Reviews number (MathSciNet)
MR2604087

Zentralblatt MATH identifier
1192.14017

Subjects
Primary: 14F45: Topological properties
Secondary: 14K22: Complex multiplication [See also 11G15] 14J28: $K3$ surfaces and Enriques surfaces 14H50: Plane and space curves

Keywords
Conjugate varieties K3 surfaces lattice arithmetic Zariski pairs

Citation

Shimada, Ichiro. Non-homeomorphic conjugate complex varieties. Singularities — Niigata–Toyama 2007, 285--301, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610285. https://projecteuclid.org/euclid.aspm/1543448022


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